Basis of the Principal Informative Components for signal estimation problems

The given paper is further development of papers [1] – [3], in which method of the Principal Informative Components (PIC) have been proposed. The PIC-method provides decreasing of estimation error in signal reconstruction problems. The method also can be used for problems of a source coding. PIC-technique is based on using of properties of eigenfunctions of Fisher´s information operator with applying of selection procedures for most informative components. Structures of the Fisher matrix for typical signal estimation problems are investigated. The initial equations for the PIC-basis are obtained with reference to the tasks of linear estimation, extraction of signal at noise background and for problem of signal demodulation. The connection of the PIC-method with Karhunen-Loeve expansion and singular values decomposition is shown.